The Bottom of the Spectrum of Time-Changed Processes and the Maximum Principle of Schrödinger Operators

Masayoshi Takeda

doi:10.1007/s10959-016-0734-0

The Bottom of the Spectrum of Time-Changed Processes and the Maximum Principle of Schrödinger Operators

Masayoshi Takeda

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

We give a necessary and sufficient condition for the maximum principle of Schrödinger operators in terms of the bottom of the spectrum of time-changed processes. As a corollary, we obtain a sufficient condition for the Liouville property of Schrödinger operators.

Original language	English
Pages (from-to)	741-756
Number of pages	16
Journal	Journal of Theoretical Probability
Volume	31
Issue number	2
DOIs	https://doi.org/10.1007/s10959-016-0734-0
Publication status	Published - 2018 Jun 1

Keywords

Dirichlet form
Liouville property
Maximum principle
Schrödinger form
Symmetric Hunt process

ASJC Scopus subject areas

Statistics and Probability
Mathematics(all)
Statistics, Probability and Uncertainty

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10.1007/s10959-016-0734-0

Cite this

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title = "The Bottom of the Spectrum of Time-Changed Processes and the Maximum Principle of Schr{\"o}dinger Operators",

abstract = "We give a necessary and sufficient condition for the maximum principle of Schr{\"o}dinger operators in terms of the bottom of the spectrum of time-changed processes. As a corollary, we obtain a sufficient condition for the Liouville property of Schr{\"o}dinger operators.",

keywords = "Dirichlet form, Liouville property, Maximum principle, Schr{\"o}dinger form, Symmetric Hunt process",

author = "Masayoshi Takeda",

note = "Funding Information: The author was supported in part by Grant-in-Aid for Scientific Research No. 26247008(A) and Grant-in-Aid for Challenging Exploratory Research No. 25610018, Japan Society for the Promotion of Science. Publisher Copyright: {\textcopyright} 2017, Springer Science+Business Media New York.",

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AU - Takeda, Masayoshi

N1 - Funding Information: The author was supported in part by Grant-in-Aid for Scientific Research No. 26247008(A) and Grant-in-Aid for Challenging Exploratory Research No. 25610018, Japan Society for the Promotion of Science. Publisher Copyright: © 2017, Springer Science+Business Media New York.

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N2 - We give a necessary and sufficient condition for the maximum principle of Schrödinger operators in terms of the bottom of the spectrum of time-changed processes. As a corollary, we obtain a sufficient condition for the Liouville property of Schrödinger operators.

AB - We give a necessary and sufficient condition for the maximum principle of Schrödinger operators in terms of the bottom of the spectrum of time-changed processes. As a corollary, we obtain a sufficient condition for the Liouville property of Schrödinger operators.

KW - Dirichlet form

KW - Liouville property

KW - Maximum principle

KW - Schrödinger form

KW - Symmetric Hunt process

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The Bottom of the Spectrum of Time-Changed Processes and the Maximum Principle of Schrödinger Operators

Abstract

Keywords

ASJC Scopus subject areas

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